Forecasting the spatial and temporal charging demand of fully electri ﬁ ed urban private car transportation based on large-scale traf ﬁ c simulation

(cid:1) Large-scale traf ﬁ c simulation


A B S T R A C T
To support power grid operators to detect and evaluate potential power grid congestions due to the electrification of urban private cars, accurate models are needed to determine the charging energy and power demand of battery electric vehicles (BEVs) with high spatial and temporal resolution.Typically, e-mobility traffic simulations are used for this purpose.In particular, activity-based mobility models are used because they individually model the activity and travel patterns of each person in the considered geographical area.In addition to inaccuracies in determining the spatial distribution of BEV charging demand, one main limitation of the activity-based models proposed in the literature is that they rely on data describing traffic flow in the considered area.However, these data are not available for most places in the world.Therefore, this paper proposes a novel approach to develop an activity-based model that overcomes the spatial limitations and does not require traffic flow data as an input parameter.Instead, a route assignment procedure assigns a destination to each BEV trip based on the evaluation of all possible destinations.The basis of this evaluation is the travel distance and speed between the origin of the trip and the destination, as well as the car-access attractiveness and the availability of parking spots at the destinations.
The applicability of this model is demonstrated for the urban area of Berlin, Germany, and its 448 sub-districts.For each district in Berlin, both the required daily BEV charging energy demand and the power demand are determined.In addition, the load shifting potential is investigated for an exemplary district.The results show that peak power demand can be reduced by up to 31.7% in comparison to uncontrolled charging.

Introduction
Man-made climate change can be slowed down if greenhouse gas emissions are reduced quickly and drastically.The signatories to the 2015 Paris Climate Agreement have therefore committed to reducing their greenhouse gas emissions to such an extent that the man-made temperature increase is limited to below 2 C [1].A key driver of this decline is the decarbonization of the transport sector.The European Union, for example, has agreed on an emission limit of 95 g CO 2 /km for passenger cars registered in 2021 [2].As a result, private passenger cars with internal combustion engines (hereinafter referred to as internal combustion engine vehicles (ICEVs)) are being replaced by passenger cars with alternative drive systems, primarily battery electric passenger cars (hereinafter referred to as battery electric vehicles (BEVs)).Without reinforcement of the electric grid infrastructure, the resulting additional demand for electrical energy and power may cause congestion in the power supply [3,4].To enable electric grid operators to identify possible congestions in the grid, accurate models are needed that predict the spatial and temporal energy and power demand resulting from the electrification of private ICEVs.Typically, e-mobility traffic simulations are used for this purpose: The authors of [5] develop a traffic simulation to forecast the spatial and temporal distribution of the charging energy demand of an urban area.In their method, they first divide the area into different functional areas (e.g., residential, work, shopping and entertainment) and assign a certain number of BEVs to each functional area.Using the known geographic origin of each BEV trip, the destinations are randomly selected.Based on the geographic location of the destinations, arrival and departure times, and travel distances, the spatial and temporal distribution of BEV charging demand is determined.However, this spatial distribution is highly inaccurate due to the random selection of destinations.Each functional area is different from the others (e.g., number of employees or number of available parking spaces) and therefore has a different probability of attracting trips which is not considered.
In [6], the authors simulate the spatial and temporal distribution of charging energy demand for an artificial city consisting of a city center, suburban areas, and connecting highways.All simulated individuals and their vehicles make a round trip that begins in a suburb and then travels to a randomly selected location in the city center and back.At each stop, the individuals decide whether to charge their vehicles, depending on their current state of charge (SOC).Based on the resulting charging demand of the vehicles at the different locations, the charging times are determined, which allows the spatial and temporal distribution of the charging demand to be determined.Due to the assumption that all vehicles make two trips per day and travel to a random location in the city, both the spatial and temporal distribution of charging demand are highly inaccurate.
For 11 districts in the city of Reykjavík, Iceland, the authors of [7] use a traffic simulation to determine the spatial and temporal distribution of BEV energy demand.The authors do not divide Reykjavík into 11 districts themselves, but use an existing classification created by official bodies.To determine the energy demand per district, the daily distances of the combustion engine vehicles and the arrival times of the vehicles at the places of residence are first extracted from a travel survey (travel surveys are obtained by surveying households in a geographic area about their activities and trips on reference days).The conventional cars are then replaced by a reference BEV with 60 kWh battery capacity and an average energy consumption of 0.2 kWh/km.All vehicles are assumed to be charged at home at the end of the day, as this charging scenario is expected to have the largest impact on the power grid.Since only arrival times at residences and the geographic locations of the residences are determined, the method can only determine the spatial and temporal distribution of charging demand, assuming that charging occurs exclusively at the residences.This does not reflect reality.
Another approach for forecasting the spatial and temporal BEV charging demand distribution is to use an activity-based mobility model [8][9][10][11][12].Activity-based models are particularly well suited for simulating the energy and power demand of BEVs because they capture the relationship between activities and mobility patterns, which can be used to determine the parking times of vehicles at different locations [13].Energy and power demand can then be estimated by applying charging scenarios.In activity-based mobility models, individual full-day travel schedules are generated for each person in the considered area.The assumption for this generation is that a person's activity and travel patterns depend on the person's characteristics (e.g. the place of residence, income, age, household and other social structures).
The travel schedules (also referred to as mobility profiles) consist of a sequence of activities at different locations and trips between these activities.They are usually generated based on a detailed travel survey [8][9][10][11].Travel surveys are conducted by interviewing households in a geographic area about their activities and trips on reference days, which allows the determination of the daily travel patterns of the population in the studied area.
In Fig. 1 an example of a mobility profile of a person is depicted.The person starts with its car at its "Home" location and goes shopping and works during the day, before arriving back home at 17:15.The daily distance covered is 45 km in total.
An activity-based model is used by the authors of [8] to determine the spatial and temporal BEV charging demand of electric cars in the Flemish region, Belgium.The basis of the determination is the number of vehicles in each district in the region, which are replaced by electric reference vehicles of three different vehicle size classes.The authors do not divide the Flemish region into districts themselves, but use an existing classification created by official bodies.For each vehicle, a mobility profile is generated using a detailed travel survey.Based on the average consumption of the reference BEVs, the arrival and departure times, and the travel distances of the BEVs, the spatial and temporal distribution of charging demand is determined.However, this spatial distribution is inaccurate because it is assumed that the proportions of the three vehicle size classes are the same in all districts.In general, larger and heavier vehicles have higher energy consumption than smaller and lighter vehicles.Thus, if the individual distribution of vehicle size classes in the districts is not taken into account, the charging demand will be underestimated in districts with many large vehicles and overestimated in districts with many small vehicles.
The authors of [9] determine the spatial and temporal BEV charging demand for Singapore using an activity-based model.They first determine the number of current internal combustion engine cars in each district, which are then replaced with electric reference vehicles.The authors do not divide Singapore into districts themselves, but use an existing classification created by official bodies.A mobility profile is created for each vehicle based on a detailed travel survey.These mobility profiles and a vehicle dynamics model are used to determine the temporal and spatial distribution of BEV charging demand in Singapore and its districts.Similar to the method developed in [8], the proportions of vehicle size classes are assumed to be the same in all districts.Therefore, the spatial distribution of charging demand is inaccurate, as previously justified.
For the Seattle metropolitan area, USA, the authors of [12] use an activity-based model to investigate how the current ICEV driving behavior of the population can be electrified.The current driving behavior of the population is derived from extensive GPS measurements in conventional vehicles.A mobility profile is created from this data for each vehicle in the area under consideration.The conventional vehicles are then replaced by a reference BEV with an average consumption of 0.186 kWh/km and a range of 161 km (100 miles).Based on the BEV consumption and mobility profiles of the BEVs, the temporal and spatial distribution of the charging demand can be determined.However, since only one reference vehicle is used, the determined spatial distribution is inaccurate.In general, larger and heavier vehicles have higher energy consumption than smaller and lighter vehicles.If vehicle size is not taken into account, the charging demand will be underestimated in districts with many large vehicles and overestimated in districts with many small vehicles.
This paper makes two important contributions to the literature.As shown, the studies proposed in the literature have limitations that lead, in particular, to inaccuracies in the identified spatial distribution of BEV charging demand.Therefore, this paper develops an activity-based mobility model that overcomes these spatial limitations.
In activity-based models, a person's destination choice is usually determined based on traffic flow data between subareas of the area under consideration.These traffic flow data can be obtained from extensive GPS measurements, as in reference [12], but are usually derived from detailed travel surveys.However, to derive traffic flows, the input data must be available at an extremely high level of detail.These detailed datasets are usually not available for most regions of the world because they are very expensive to generate.To address this problem, in this paper we develop an activity-based mobility model that does not rely on traffic flow data.In contrast, we propose a model based on open data, which ensures its traceability, reproducibility, and transferability.The developed model is applied to forecast the spatial and temporal distribution of charging energy and power demand resulting from the complete electrification of private ICEVs in an urban area.The use case of this paper is Berlin, Germany, with a total number of 1,045,000 [14] private passenger cars.
The developed model consists of three main parts which are discussed in Section 2. Two of these three parts have already been presented in previous articles [15,16].In this paper, we present the development of the third part in Section 3, thereby completing the model and enabling the determination of the spatial and temporal charging energy and power demand.The charging scenarios investigated are discussed in Section 4. The results are presented and analysed in Section 5. Finally, the main conclusions of this paper are presented in Section 6.

Three-step model for estimating the charging demand of BEVs using open data
The three-step model for estimating the spatial and temporal distribution of BEV charging demand is depicted in Fig. 2. The model is applied to the urban area of Berlin, Germany, and its 448 sub-districts, which are referred to as "Lebensweltlich orientierte R€ aume" (Eng.: neighbourhood-oriented districts, abbr.: LORs).The LOR classification is Fig. 2. Three-step model for estimating the spatial and temporal energy and power demand from the electrification of private ICEVs.an official classification of the Berlin administration.Within each LOR, the structure of the included buildings and the socio-economic status of the inhabitants are similar.The LORs are usually separated from each other by major roads, rivers or rails [17,18].The first part of the model was developed in [15] and is summarized below.In [15], the current conventional vehicle fleet in the districts (in total, 1,045,000 private cars in Berlin [14]) is first completely electrified.For electrification, data on motorization levels and population density are used to determine the spatial distribution of the vehicles in the considered area.The spatial distribution of household income is then used to determine the spatial distribution of vehicle size classes in the districts.This yields the number and size of vehicles for each district, which are then replaced with reference electric vehicles.For the replacement of the current ICEV fleet 12 electric passenger cars are used which are depicted in Table A.1.For each reference vehicle, Table A.1 also specifies its energy consumption per 100 km and its battery capacity.The average consumption is divided into inner-city trips, characterised by distances of less than 20 km and outer-city trips.The values of the energy consumption and battery capacity are based on test drives of the "Allgemeine Deutsche Automobil Club" (ADAC), a German motoring association, and already include charging losses [19].
Subsequently, a travel survey is used to determine vehicle-based mobility profiles.Vehicle-based mobility profiles are generated (instead of person-based ones) because they realistically represent multiple uses of the same vehicle by multiple people (e.g.families).The survey data is limited.While it is possible to determine the driving behaviour of the population from this data, it is not possible to derive activity-and timedependent traffic flows between districts.Therefore, the vehicle-based mobility profiles generated do not contain information about the geographic location where the vehicle is parked while the BEV user is performing an activity.Unlike travel surveys, from which traffic flows can be derived, these limited travel surveys are widely available.Fig. 3 shows example vehicle-based mobility profiles for the 1,045,000 private BEVs in Berlin.It can be seen that some vehicles are not driving on the simulated day and each vehicle is assigned an individual daily schedule.
Based on these preliminary mobility profiles, the spatial and temporal distribution of charging energy and power demand in Berlin is determined.However, there is one major limitation to the results.Since the locations of the activities are not known, the charging demand can only be determined for the assumption that charging occurs exclusively at the residences of BEV owners.
To overcome this limitation, the geographic location where the vehicle is parked while the BEV user is performing an activity needs to be determined.An important input variable in this determination is the car-access attractiveness of the districts.The determination of the car-access attractiveness is the second part of the model.It was developed in [16] and applied to the 448 LORs of Berlin.The car-access attractiveness is a measure of how attractive buildings and districts are to drive to by car for a particular activity.A high attractiveness indicates that a location is highly likely to be accessed by car, while a low attractiveness means that the location is more likely to be accessed by another mode of transportation.The car-access attractiveness is determined based on the number of available parking spots in the districts, the distance of the buildings in the district from the parking spots, and their distance to public transportation.
The last part of the model combines the results of Parts I and II and corresponds to the scope of this paper.A route assignment method is developed that is used to assign an appropriate route to each BEV to determine the unknown geographic destinations of BEV trips (in the following, a BEV's route is referred to as the sequence of the BEV's locations, not the route the vehicle chooses on the road to get from an origin to a destination).This allows the determination of the spatial and temporal distribution of charging energy demand of an urban region, taking into account charging for all activities.
The basis of this route assignment method is a destination choice model.In destination choice models, the most plausible destination among all possible destinations is selected for each BEV trip based on predefined criteria.The most common criteria are the attractiveness of the destination and the distance between origin and destination, which are usually combined in a gravity model [20][21][22][23][24].The basic principle of the gravity model is the assumption that a traffic cell behaves like a gravitational point, i.e. the more mass (attractiveness) a cell has (e.g.number of employees or sales area), the higher its gravitational pull.As the distance increases, the cell's gravitational pull decreases [25].Analogous to the gravity model, we also use the distance between origin and destination and the attractiveness of the destination for the destination choice model of this paper.
However, we do not use the number of employees or the sales area to describe the attractiveness of a district, but the car-access attractiveness developed in Part II.This is because the availability of parking spots is neglected.This neglect means that, for example, shopping centers with a large sales area and companies with many employees are considered very attractive, regardless of whether sufficient parking infrastructure is available.However, it is obvious that it is not possible to park at a location where there is no parking infrastructure.
Additionally, to these two criteria, the travel speed between origin and destination is considered as a criterion, as it has a strong influence on the choice of the destination itself [21,[26][27][28].As fourth criterion the time-dependent availability of parking spots in the districts is considered.This is necessary to prevent individual districts with high car-access attractiveness from being allocated all vehicles.
We apply the route assignment method to the mobility profiles generated for BEVs in the urban area of Berlin, Germany, and its 448 subdistricts (LORs) in Part I.These mobility profiles show that in Berlin 41.5% of the trips lead to the BEV owner's residence (18.3 h average parking time), 17.7% to work locations (7.5 h average parking time) and 8.3% to Fig. 3. Vehicle-based mobility profiles of the population under consideration.shopping locations (50 min average parking time).Other activities such as leisure activities, visits to the doctor etc., each account for less than 2% of the trips [15,29].From these findings, we conclude that the home, workplace, and shopping locations are where most charging events will occur in the future.Therefore, the locations of shopping and work activities are determined in this paper.However, the method is designed to be extensible so that additional activities can be easily integrated.Since Berlin cannot be considered a closed unit, commuters must be taken into account.The total number of commuters in and outbound is derived from [30][31][32].Vehicle-based mobility profiles are created for inbound commuters analogous to the procedure described in [15] for Berlin; the driving behaviour of inbound commuters is described in [32][33][34][35][36].
Based on the routing results, the spatial and temporal distribution of BEV charging energy and power demand is determined for four different charging scenarios.The results are then used to investigate the load shifting potential in an exemplary LOR.

Methodology
The goal of the route assignment method is to determine the most likely destination for each vehicle trip.To achieve this goal, all possible destinations must be evaluated and compared.In this paper, the evaluation of each destination is based on four criteria according to the weighted sum model, which is commonly used for multicriteria decision analysis [37].The basic concept behind the weighted sum model is the additive utility assumption.If all criteria are measurable with the same unit, the best alternative is the one with the largest cumulative value R [37,38].The value R of each alternative j can be computed as where n is the number of criteria, k i is the value for the criterion i and w i is the individual weighting-coefficient of the criterion i.In general, the higher the value of w i , the more important the criterion.Typically, the weighting-coefficients are normalized so that their sum is one [37].
As explained in the previous section, the four selected criteria for rating a destination are the distance and travel speed between districts, as well as the car-access attractiveness and the availability of parking spots in the districts.Since these criteria do not have the same unit, a dimensionless rating value k is used for each criterion, ranging from 1 to 10.The derivation of the rating values of the criteria is explained in detail in Section 3.1-Section 3.4.Section 3.5 then presents the route assignment method.The methodological approach is applied to Berlin and its 448 sub-districts (LORs), in the following sections.

Criterion 1: travel distance
The mobility profiles of the BEVs are the basis for route assignment.As shown in Fig. 3, they consist of a sequence of activities at different locations and trips between these activities.For each trip, the travel distance is known.Since the origin district of each trip is also known (as explained in Section 3.5), all possible destination districts can be determined and rated based on the distance travelled.For this evaluation, we determine the frequency distribution of travel distances for each origindestination LOR combination (448 LORs yield 200,704 combinations).
The basis for this determination is a self-generated dataset containing 50 randomly distributed coordinates on roads in the LOR for each LOR (highways, forest roads, etc. are excluded).This dataset is used to calculate the travel distances between the 50 origin coordinates and the 50 destination coordinates for each O-D LOR combination.Thus, a total of 2,500 travel distances are determined for each combination.The calculation of the driving distance between two coordinates is done via the freely useable OpenRouteService Time-Distance Matrix API [39].
The 2,500 values of each combination form the basis for the evaluation of the travel distances.We assume that the probability of traveling to a destination LOR decreases as the deviation between the travel distance and the median of the 2,500 values increases.The median is used instead of the average because it is more robust to outliers.
In order to convert the 2,500 values into a dimensionless rating, they are sorted in ascending order and divided into 20 equal-sized data bins, i.e. 125 values are assigned to each bin.Similar to [40,41], each bin is then assigned a rating value k d between 1 and 10.A rating value k d ¼ 10 means that it is very likely to travel from the known origin to the destination LOR, and correspondingly very unlikely for k d ¼ 1.
The assignment of rating values to bins is exemplified for one origin LOR and three possible destination LORs in Fig. 4. The location of the origin LOR and the destination LORs in Berlin is shown in Fig. 4(a).In Fig. 4(b), the division of the calculated driving distances into the 20 bins and the rating value assigned to them is shown.It can be seen that the further the driving distances are from the distance median, the lower the rating value obtained.For an example travel distance of 9.5 km, it can be determined which of the three destination LORs is the most likely destination (when starting from the origin LOR).It can be seen that destination LOR 1 is not a possible destination, because it cannot be reached from the origin LOR with a travel distance of 9.5 km.The distance median of O-D LOR combination 2 is 8.3 km which is close to 9.5 km.Therefore, the destination LOR 2 receives a medium rating value k d of 6.For O-D LOR combination 3 the distance median is 13 km.Accordingly, at a distance of 9.5 km, destination LOR 3 receives a low rating value k d of 2. Therefore, it is more likely to travel to destination LOR 2 than to destination LOR 3, considering the travel distance criterion.

Criterion 2: travel speed
The travel speed between an origin and a destination is a key criterion in destination choice models [21,[26][27][28].The basic assumption is that the higher the travel speed between an origin and a destination, the more likely it is to travel to the destination.
Although it would be possible to describe the travel speed for each O-D LOR combination with a mean value, we use frequency distributions to achieve greater accuracy.The basis of these frequency distributions are the 2500 travel distances computed for each O-D LOR combination in Section 3.1.Using the OpenRouteService Time-Distance Matrix API, it is possible to calculate the associated travel time and thus travel speed for each of the travel distances.
For two origin-destination LOR combinations, the 2,500 data tuples obtained are shown as a scatter plot in Fig. 5(a).In particular, for the origin-destination LOR combination 2, it can be seen that higher travel distances lead to higher travel speeds.This is due to the fact that increasing travel distance increases the likelihood of using major roads or highways that allow higher travel speeds.To reflect this correlation, the evaluation of travel speed between origin and destination must be based on travel distance.
Since different travel speeds occur for the same distance, the average speed of each of the 20 travel distance ranges identified in Section 3.1 is determined for each O-D LOR combination.This average speed is shown as solid green line in Fig. 5(a).
For the 9.5 km travel distance used as an example in Section 3.1, the average travel speed for the O-D LOR combination 2 is 28 km/h, as can be seen in Fig. 5(a).To derive a dimensionless rating value for this travel speed, it is compared to the distribution of travel speeds for all of Berlin.
To derive this Berlin distribution, the 2,500 calculated travel speeds for all origin-destination-LOR combinations are first combined into one dataset and sorted in ascending order.Then, the values are divided into 10 equal-sized data bins, i.e. 10% of the values are assigned to each bin.Similar to [40,41], a dimensionless rating value k s is then assigned to each bin.As shown in Fig. 5(b), the 10% lowest speeds in Berlin are assigned a rating value k s of 1 and the 10% highest are assigned a rating value of 10.This classification means that the higher the travel speed between an origin and a destination, the more likely it is to travel to the destination.
In Fig. 5(b) it can be seen that 28 km/h is a rather low speed in Berlin.This results in a low rating value k s of 2. Therefore, it is unlikely to travel from the origin LOR to destination LOR 2, considering the travel speed criterion.

Criterion 3: car-access attractiveness
The attractiveness of locations is another key factor in destination choice models [22][23][24].The higher the attractiveness of a location, the  higher is the probability for trips to that location.In this paper we use an attractiveness description of locations, specifically developed for access by car.This car-access attractiveness provides information on how attractive it is to drive to a particular LOR to perform a particular activity.The determination of the car-access attractiveness of Berlin's LORs is described in detail in [16].
In [16] car-access attractiveness is first determined for shopping and work trips at the building level, and the results are then aggregated at the LOR level.For shopping trips, the car-access attractiveness is based on three criteria: the number of customer parking spots per sales area of the building, the distance of the parking spaces to the building, and whether there is a charge for using the parking spaces.For work trips, the car-access attractiveness is determined based on the number of employee parking spots per employee of the building, the distance of the parking spaces to the building, and the average distance of the building to the nearest public transportation stop.
Car-access attractiveness is described in [16] with a dimensionless value between 1 and 5, where a value of 5 indicates high attractiveness.In this paper, the scale is adjusted to the other rating values by multiplying by 2. The result is a rating value k a between 1 and 10 for each LOR, which describes its car-access attractiveness.

Criterion 4: availability of parking spots
A rating value k c is determined to evaluate the parking availability in the LORs.Its values vary from 1 (if less than 10% of parking spots are available) to 10 (if at least 90% of the parking spots are available).The total number of customer and employee parking spots per LOR, available for shopping or work activities, is determined along with car-access attractiveness in [16] using OpenStreetMap geodata.
In [16], roadside parking spots that are not labelled in the Open-StreetMap dataset are not considered.To determine the additional number of roadside parking spots available for shopping and work trips, we first determine the total number of roadside parking spots for each LOR, analogous to the method described in [42].
Then, roadside parking spots that are permanently occupied by commercial or private vehicles are excluded.In the city of Berlin, 40% of the population has access to private parking (e.g.garages), while the remaining 60% park their cars on roadside parking spots when they are at home [34].63% of commercial vehicles are parked at roadside parking spots [34].As a result, especially in densely populated LORs, many roadside parking spots are occupied at night and in the morning and become vacant when vehicles leave.Consistent with [16] we assume that 50% of vacant roadside parking spots can be used for activities that are not considered in this paper, such as leisure activities or doctor visits.The remaining 50% are equally useable for work and shopping activities.

Route assignment method
The input data for the route assignment method are the mobility profiles of the Berlin vehicles and the inbound commuter vehicles.While the home locations of the vehicles (i.e., the residences of the vehicle owners) are known, the locations where the other activities are performed are unknown.Therefore, the goal of the route assignment method is to determine the most likely destination LOR for each vehicle trip.
The route assignment method distinguishes between two different types of mobility profiles, depending on whether the first trip starts at the residence of the BEV's owner.For those BEVs whose first trip begins at home, an iterative process is performed, as shown in Fig. 6.For BEVs that do not start at home, the route assignment is described at the end of this section.
In Step (1), all possible routes are determined for each vehicle.The determination is based on the individual travel distances of the trips and the minimum and maximum travel distances of the O-D LOR combinations (determined in Section 3.1).
The selection of the most plausible route is time-driven, i.e., routes are determined trip by trip rather than vehicle by vehicle.This means that destinations are assigned chronologically based on the starting time of each trip for each vehicle.This approach allows considering the availability of parking spots as a time-dependent parameter.
When the first trip of a vehicle starts and is to be assigned to a destination LOR, it is first checked for each possible destination whether its maximum BEV intake capacity has already been reached.The maximum intake capacity of a LOR for work activities is 85% of its number of employees.The number of employees per LOR was derived in [16].85% is derived from the ratio of full-time and part-time employees according to [43,44].
The maximum BEV intake capacity per LOR for shopping activities is 10% of its sales area.This number is derived from [16], where it was shown that the average Berlin supermarket provides one parking spot per 10 m 2 of sales area.
The LORs to which a vehicle can be assigned are then rated according to Eq. (2) in Step (2).For shopping and work trips, the evaluation of the single destination LOR R LOR is based on the four criteria introduced in Section 3.1-Section 3.4.As we explained in Section 2, this paper analyzes the spatial and temporal BEV charging energy demand considering home and workplace charging, as well as opportunity charging at shopping locations.For all other activities, vehicle charging is not considered.Therefore, a reduced version of Eq. ( 2) is used to rate a destination LOR for "other" activities.However, this reduced version still ensures that a plausible destination LOR is determined for the trip.

Work or shopping trips:
Following the rating of all possible destination LORs for the first trip, the route assignment procedure continues depending on whether another trip takes place.If no further trip takes place, the destination LOR with the highest rating according to Eq. ( 2) is selected (Step (5) in Fig. 6).Since a parking spot in the selected LOR is now occupied, the criterion "availability of parking spots" for this LOR is updated considering the parking time of the vehicle (Step (6) in Fig. 6).
If another trip takes place, it is also considered when determining the destination LOR for the first trip.The necessity of this consideration is illustrated in Fig. 7(a) for two destinations D1 and D2.It can be seen, that both destinations can be reached with the first trip.The rating of destination D2, R LOR ¼ 9.2, is significantly higher than the rating of destination D1, R LOR ¼ 4.4.However, the subsequent possible trips from D2 to destination D4 or D5 are very unlikely, as indicated by the very low ratings R LOR of 1.2 and 1.6, respectively.
Therefore, to avoid selecting a destination for the first trip that is an unsuitable origin for the second trip, the ratings of the possible second trips are also taken into account.For this purpose, first their average rating (Step (3)) is calculated as 1.4.Then, in Step (4), the average rating of the first and second trip R LOR, a is determined according to Eq. (3).
In Eq. (3), R LOR, i is the rating of the destination LOR for trip i, while R LOR, iþ1 is the average rating of the destination LORs for subsequent trip i þ 1.As can be seen in Fig. 7(b), the average rating R LOR,a for destination D2 is 5.3.For destination D1, R LOR,a ¼ 5.7.Consequently, destination D1 is selected as the destination of the first trip.After this selection, in Step (6), the criterion "availability of parking spots" is updated for the selected LOR, taking into account the parking time of the car.Since the second trip does not lead home, the route assignment procedure starts again and the destination of the second trip is determined.For vehicles whose starting location of the first trip is unknown, the described route assignment procedure cannot be performed because it requires a known starting location.Therefore, the starting location must first be determined.For this purpose, all possible routes of the vehicle are first determined.This is possible because it is known that the last trip of the vehicle ends at the home location.If the first trip is to be assigned to a destination LOR, the possible destination LORs for all possible origin LORs are rated analogously to Step (2).If the vehicle makes a second trip, the possible destination LORs for the second trip are also rated (Step (3)).Then, the origin-destination LOR combination with the highest rating is selected, which means that both the destination LOR and the origin LOR are determined for the first trip of the vehicle.Since the starting location of the vehicle's first trip is now known, the route assignment procedure described in Fig. 6 can be applied starting from Step (6).

Investigated charging scenarios
In Berlin 41.5% of the trips lead to the BEV owner's residence (18.3 h average parking time), 17.7% to work locations (7.5 h average parking time) and 8.3% to shopping locations (50 min average parking time).Other activities such as leisure activities, visits to the doctor etc., each account for less than 2% of the trips [15,29].From these findings, we conclude that the home, workplace, and shopping locations are where most charging events will occur in the future and which are therefore considered in the charging scenarios.
For these locations four different types of parking spots are considered (see Section 3.3 and Section 3.4): 1. Employee parking spots, used for parking while at work; 2. Customer parking spots, used for parking while shopping; 3. Private parking at the residences, used for parking while at home; 4. Roadside parking spots, that can be used for parking while at work and shopping and by BEV owners who do not have a private parking spot at their residence.
In this paper, four different charging scenarios are investigated.Three base charging scenarios which are described in Section 4.1 and one datadriven charging scenario which is described in Section 4.2.

Base charging scenarios
Home-charging scenario: The state of charge (SOC) of each BEV is 100% before its first trip.Each BEV starts charging immediately upon arrival at home and does not end until the vehicle is fully charged or starts driving again.As some inbound commuters drive long distances, these vehicles cannot travel their daily distance without recharging.Therefore, these vehicles are charged at the commuter's workplace.
Work-charging scenario: The state of charge (SOC) of each BEV is 100% before its first trip.Each BEV starts charging immediately upon arrival at its place of work and at home and does not end until the vehicle is fully charged or starts driving again.Many vehicles are not used for a trip to work on the simulated day.In order not to neglect the energy demand of these vehicles and to allow a comparison between the home-charging and work-charging scenario, the vehicles can also be charged at home.
Opportunity-charging at shopping locations: The state of charge (SOC) of each BEV is 100% before its first trip.Charging starts immediately upon arrival at a shopping location and at home and does not end until the vehicle is fully charged or starts driving again.As justified above, home charging is required for comparison with the other scenarios.Analogous to the Home-charging scenario, the vehicles of commuters who travel long distances are recharged at workplaces.
The maximum available charging power is set to 11 kW for private parking and roadside parking spots in accordance with [45].For charging at employee parking spots, the maximum power is limited to 22 kW in accordance with real world applications [46,47].For customer parking spots, the maximum power is limited to 50 kW which is in accordance with real world applications as well [48][49][50].
The three charging scenarios presented should be understood as extreme cases.Setting the SOC to 100% before the first trip is necessary to ensure comparability between the scenarios.
The maximum charging power that BEVs can use is SOC-dependent.BEVs can usually retrieve the highest charging power at a SOC between 20% and 80%.At a higher SOC, the useable charging power decreases significantly, resulting in longer charging times.
In Berlin, the average daily distance of private passenger cars is 59.5 km (parked vehicles excluded) [15].Consequently, the SOC of the vehicles usually ranges between 80% and 100% if the above charging scenarios are applied.In order not to massively overestimate the charging times, we assume for the base charging scenarios that 95% of the maximum charging power can be retrieved constantly by the BEVs regardless of their SOC.The reduction factor of 95% is taken from [45].

Data-driven charging scenario
The spatial and temporal distribution of BEV charging demand resulting from the three base-charging scenarios can be used for extreme value analyses.The actual future charging behavior and thus the future distribution of BEV charging demand is unknown.
One way to model the future charging behavior is to assume that the future charging behavior corresponds to the current BEV charging behavior.Since no BEV charging data is available for Berlin, we use charging data from 41 private BEVs in Beijing, China.The data and its analysis are described in [51].For the development of the data-driven charging scenario, the authors of this paper were provided with the raw data set.The data from Beijing are used because the driving behavior of the 41 BEVs and the driving behavior of the BEVs in Berlin are very similar.In Beijing, for example, 80% of vehicle trips are shorter than 21 km, compared to 81.1% of vehicle trips in Berlin.In addition, the average daily distance of non-parked vehicles is similar.In Berlin, this distance is 53.2 km while it is 49.8 km in Beijing.Furthermore, in Beijing 85.2% of the total daily distances are below 80 km, while 82.3% are computed for Berlin in [15].It is important to note that charging behavior depends not only on driving behavior, but also on the available charging infrastructure (number, locations, charging power).It is unclear whether the charging infrastructure available to the 41 BEVs in Beijing is comparable to that in Berlin.To reduce the resulting uncertainty, charging behavior is not modeled by predetermined statements (e.g., 80% of charging events occurs at home with 11 kW), but by two driving behavior-based probability distributions derived from the dataset.These distributions are depicted in Fig. 8. Fig. 8(a) shows the relative frequency distribution of SOC at the first trip of the day of Beijing BEVs.The Beijing dataset reveals, that vehicles that use a greater share of their battery capacity over the course of a day (i.e., tend to drive longer distances), have a higher SOC before their first trip of the day.To map this, one distribution is determined for vehicles that use more than 50% of their battery capacity during the day.The other for vehicles that consume less than 50% of their battery capacity during the day.For both cases it can be seen that it is most likely to start the first trip of the day with a SOC of 100%.Fig. 8(b) shows the charging probability of Beijing BEVs for different rechargeable SOC differences.The rechargeable SOC difference describes the difference between an initial SOC and an end SOC up to which charging is possible during parking time.A SOC of 10% before charging and a rechargeable SOC difference of 60% would for example result in a SOC of 70% after charging.As can be seen in Fig. 8(b), 78% of BEV users charge their vehicle when the rechargeable SOC difference is 60%.
Based on these two probability distributions, the data-driven charging scenario is developed, which is shown schematically in Fig. 9.It is applied to each BEV individually.
In Step (1) the share of battery capacity used over the course of a day is determined.In Step (2), depending on this result, the SOC before the first trip is determined using Fig. 8(a).In Step (3) the energy consumption of the next trip is calculated.If the SOC, determined in Step ( 2) is not sufficient to complete the next trip, Step (2) is executed again.If the SOC is sufficient, it is examined whether charging is possible at the destination of the trip.As justified in the introduction of this section, this paper only considers charging at home, at work, and while shopping.If the vehicle travels to another destination, it is not charged.If the BEV can be charged at the destination, the rechargeable SOC difference is calculated in Step (4) based on the parking time of the vehicle.Besides the parking time, the rechargeable SOC difference depends on the available charging power at the charging station and the charging curve of the BEV.The SOCdependent charging power of the reference vehicles is described by charging curves, which are shown in the Appendix (Fig. A.1).The charging curves were determined by experimental measurement [52,53].Consistent with the other charging scenarios the maximum available charging power is set to 11 kW for private parking and roadside parking spots, to 22 kW at employee parking spots and to 50 kW at customer parking spots.
In Step ( 5), the rechargeable SOC difference is used to determine whether the vehicle is recharged according to the probability distribution shown in Fig. 8(b).If the vehicle makes another trip, Step (3) is executed again.

Results and discussion
By applying the route assignment method to all vehicles, a route can be determined for each BEV.Thus, it is known which districts the BEVs travel to for their trips, as well as the parking times of the vehicles in the districts.This, in turn, enables the prediction of spatial and temporal BEV charging demand through the application of charging scenarios.
In this section, this demand is computed for the city of Berlin.For all results presented below, an identical weighting of the rating criteria is used, i.e. w d ¼ w s ¼ w a ¼ w c ¼ 0.25.In terms of destination choice, this means that all criteria are considered equally important.
This section is organized as follows: the total BEV charging energy demand for Berlin is discussed in Section 5.1.We present the spatial and temporal distribution of the charging energy demand in the Berlin LORs in Section 5.2 and Section 5.3, respectively.These results are the basis for intelligent load shifting methods.Therefore, in Section 5.4, we demonstrate for an example LOR how load shifting can reduce the grid impact of BEVs.Finally, the results are discussed in Section 5.5.

BEV charging energy demand in Berlin
In Table 1, the total BEV charging energy demand for an average working day (Monday-Thursday) in Berlin is listed for each charging scenario.Energy demand is lowest for the home charging scenario at 5,468 MWh.This is because most inbound commuters do not charge in Berlin.In the work-charging scenario, 72.9% of the BEVs' total energy demand is charged at residences.This high share compared to workplaces is due to the fact that (i) not all BEVs travel to work and are therefore still charged at their owner's residence, and (ii) vehicles that charged at work also charge each time they arrive home.The higher total demand compared to the home charging scenario is due to inbound commuters charging at their workplaces.
Similar results are observed for the opportunity-charging scenario.90.1% of the total energy demand is charged at the residences.The higher percentage compared to the work-charging scenario can be explained by the lower number of vehicles going shopping and by the fact that shopping stops are usually short and therefore the amount of energy that can be charged is limited.The higher total energy demand compared to the home-charging scenario is due to commuters shopping in Berlin.
The highest total energy demand results from the data-driven charging scenario.It is found that the energy demand at the places of work is 25.5% higher compared to the work-charging scenario.This is due to the fact that vehicles in this scenario do not start their first trip with a SOC of 100%.Especially for BEVs that only drive to work and back to the owner's home and do not perform any other activities, this leads to a high charging demand at the workplaces.In contrast, the energy demand at shopping locations is 46.9% lower compared to the opportunity-charging scenario.This is because the amount of energy that can be charged during the stops is limited due to the short parking times.As a result, many vehicles do not to charge.In the data-driven charging scenario, 61.8% of the total charging energy demand is charged at the residences.

Spatial distribution of the charging energy demand
In Fig. 10 the spatial distribution of the BEV charging energy demand in the Berlin LORs is shown for the data-driven charging scenario on an average working day.Separate figures are shown for the total energy demand as well as for the share of total energy demand charged at residences, workplaces, and shopping locations.
For the spatial distribution of energy demand at workplaces, the demand is relatively similar in the inner-city and outer-city LORs.This is because there are more employees in the inner-city LORs than in the outer-city LORs, but a higher proportion of employees in the outer-city LORs drive to work because of lacking public transportation and good parking possibilities (see Fig. 13 in [16]).
The highest energy demand at workplaces can be observed for the LOR "Motardstraβe" in western Berlin.This is due to (i) the high number of employees; (ii) the high parking ratio per capita and (iii) the proximity to a highway.As a result, the car-access attractiveness and accessibility of this LOR is very high.
Except for two LORs, the spatial distribution of energy demand at shopping locations in Berlin is also relatively homogeneous.These exceptions are the LOR "Alexanderplatz" in the center of Berlin and the LOR "Alt Tegel" in the northwest.Both districts have a significantly higher energy demand than the other LORs.The LOR "Alexanderplatz" has the largest sales area of all LORs.Several parking garages allow parking there.However, the fact that many vehicles are assigned to it in the routing process is mainly due to its central location and the very good connection via several federal highways.The LOR can therefore be  reached easily and quickly from anywhere.The high demand in the LOR "Alt Tegel", on the other hand, can be explained by the fact that the surrounding LORs have hardly any sales area as can be seen in Figure 10 in [16].Since the LOR "Alt Tegel" is easily accessible by highway access and people tend to shop close to their residences, the LOR attracts people from the surroundings to shop there.In Fig. 10(c), the spatial distribution of the charging energy demand at the residences in the Berlin LORs can be seen.LORs with high energy demand coincide with LORs with high population density, high motorization rate, and high household income.These results have already been discussed in Section 3.4 in [15].The spatial distribution of total energy demand is very similar to the distribution of the demand charged at residences.This is due to the fact that 61.8% of total demand is charged at the residences, as shown in Table 1.LORs with near zero total charging energy are sparsely populated, as they mostly consist of forests and lakes.

Temporal distribution of the charging power demand
In Fig. 11 the temporal distribution of the BEV charging power demand in the Berlin LORs is shown for all charging scenarios on an average working day.For the work-and data-driven charging scenario, it can be seen that the power demand at the workplaces mainly occurs in the morning hours, reaching its maximum around 9:00 AM and decreases thereafter.
The decrease is significantly faster for the work-charging scenario, because all vehicles are charged immediately after arrival at their user's workplace (regardless of their SOC).Since their energy demand is therefore often low, power demand drops sharply due to decrease of arriving BEVs after the start of the work day.In contrast, fewer vehicles are charged in the data-driven charging scenario, but these vehicles have a higher energy demand.Because of this higher demand, the vehicles have a longer charging time, which means that charging power is needed over a longer period of time.The power demand curve becomes wider.
Charging power demand at shopping locations reaches its maximum around 4:30 PM, both for data-driven charging and opportunity-charging scenario.This corresponds approximately to the time when people leave work.As justified in Section 5.1, the energy demand at the shopping locations is lower for the data-driven charging scenario than for the opportunity-charging scenario, resulting in a lower peak in the power demand.
The shape of the power demand curves at the residences is similar for all charging scenarios except the data-driven charging scenario and has already been discussed in Section 3.5 in [15].In contrast to the other scenarios, it can be observed for the data-driven charging scenario that the peak power demand is reached at about 2:00 AM instead of 6:30 PM.This is due to outbound commuters driving long distances to work (>85 km).Due to the longer distances and associated longer travel times, these outbound commuters return to Berlin late in the evening.Since the BEVs have travelled long distances, their rechargeable SOC difference is high and thus the probability that the BEVs will be charged is high as well.In addition, the vehicles in the data-driven charging scenario tend to have a higher energy demand than in the other charging scenarios.Therefore, the transition point where the number of BEVs that start charging is lower than the number of BEVs that finish charging is later.
For the data-driven charging scenario, the spatial distribution of charging power demand over the course of the day is shown in the Appendix (

Temporal distribution of the charging power demand with load shifting
The parking times of BEVs are usually longer than their charging times.Therefore, it is possible to shift vehicles' charging times to times when the impact on the electric grid is minimal.These load shifting investigations require knowledge of the parking location and duration of the vehicles as well as their charging requirements, which were determined in this paper.
In Berlin, 45% of private cars are parked all day.The other, used vehicles are parked on average 18.3 h per day at the owner's place of residence [15,29].Due to these long parking times, it is of particular interest to investigate the load shifting potential at the residences.Therefore, this section investigates how the BEV charging power demand can be shifted (depending on the residential load curve) to reduce the grid impact.For this purpose, a valley-filling method is used which is shown schematically in Fig. 12.As can be seen, valley-filling is done vehicle by vehicle.The individual vehicle is not charged immediately after its arrival, but at times (within its parking time) when power demand in the considered area is minimal.
The load-shifting investigation is conducted using the LOR "Heiligensee" as example, which is located on the north-western city boundary.It is selected because it has both, the highest BEV energy demand at the residences of all LORs and a very high BEV charging energy demand per resident in Berlin.The determination of the residential power demand for the LOR "Heiligensee" is described in detail in Section 3.5 in [15].In Fig. 13 the load shifting results for the home-charging and the data-driven charging scenario is presented.For both charging scenarios, it can be seen that in the case of uncontrolled charging (immediate charging upon arrival with maximum charging power), the BEV charging peak coincides with the residential evening power demand peak.The peak value is lower for the data-driven charging scenario because the total amount of energy charged at the residences is lower (see Table 1).
When load shifting is applied, the peak power demand for the homecharging scenario can be reduced by 31.7%.Due to the comparatively low charging times and the high parking times in the home-charging scenario, the BEV power demand can be distributed in such a way that the total demand in the LOR remains constant.Therefore, the peak-toaverage power ratio of a LOR, which describes the ratio of peak power demand to average power demand, is 1.0.Compared to residential power demand, the maximum power demand (residential þ BEV power demand) increases by 21.5% for controlled charging and by 77.9% for uncontrolled charging.In the data-driven charging scenario, the peak power demand can be reduced by 28.2%.Due to the longer charging times of BEVs compared to the home-charging scenario, the power demand of BEVs cannot be shifted to achieve a peak-to-average power ratio of 1.0.However, the total power demand is nearly constant.The peak-toaverage power ratio is 1.055.Compared to residential power demand, the maximum power demand increases by only 6.6% for controlled charging and by 48.4% for uncontrolled charging.
Since the load shifting investigations are conducted for a LOR with one of the highest BEV charging demands per resident, it is expected that peak power demand in most other LORs can also be significantly reduced compared to uncontrolled charging.It should be noted, however, that the results represent a theoretical ideal case and indicate the theoretically possible optimum.In a real application, the driving and parking behavior of all considered vehicles is not exactly known in advance.

Discussion
The results show that between 5,468 MWh and 6,0093 MWh of charging energy is required on an average working day in Berlin, depending on the charging scenario.At least 61.8% of this energy is charged at the residences.
Regarding the spatial distribution of energy demand at workplaces, demand is relatively similar in inner-city and outer-city LORs.Demand ranges from 0 kWh per day in LORs with no employees to 21.2 MWh per day in a LOR with many employees, high car-access attractiveness, and good accessibility.Charging energy demand at shopping locations ranges from 0 kWh per day in LORs without shopping facilities to 5.5 MWh per day in LORs that attract many shopping trips due to their location and parking situation.Charging energy demand at residences ranges from 0 kWh per day in uninhabited LORs to 40.7 MWh per day in LORs with high population and motorization levels.High demand is most prevalent in outer-city LORs.
The temporal distribution of the charging power demand is highly dependent on the charging scenario.The peak power demand ranges from 328 MW to 412 MW.The minimum power demand is between 78 MW and 169 MW.
In 2021, the peak load in the Berlin power grid was 2,119 MW [54].Assuming that this peak load coincides with the BEV peak power demand of 412 MW, this results in a 19.4% increase in peak power demand.However, there is significant load shifting potential in the LORs.As shown in Section 5.4, the peak power demand at the residences can be reduced by 28.2% through load shifting for the data-driven charging scenario.
Berlin's total electric energy demand in 2021 was 13.9 TWh [54].In this paper, we calculated a daily charging demand on an average workday (Monday-Thursday) of 5,435 MWh for the Berlin BEVs.In [15], Fig. 12. Smart charging using valley-filling approach.a charging demand of 4,730 MWh was determined for an average Saturday.Assuming that the energy demand on Fridays and Sundays corresponds to the demand on Saturdays, an annual charging energy demand of 1.87 TWh is derived for Berlin from our results.Comparing this number with Berlin's current total energy demand shows that it increases by 13.5% due to the additional BEV charging demand.
To check the validity of the results, they can be compared with the results of other studies.Due to different assumptions, differences between the results of this dissertation and the comparative studies are to be expected.Therefore, the main focus of the comparison of results is to check whether the results are in the same order of magnitude.A summary of the comparisons is presented in Fig. 14.
It is estimated, that complete electrification of all 45 million passenger cars in Germany would require 100 TWh of annual energy [55].Of this, 2.32 TWh would be required for the electrification of vehicles in Berlin.As derived above, our results for Berlin yield an annual charging energy demand of 1.87 TWh.This corresponds to 80.6% of the demand determined in [55] (see Fig. 14(a)).The difference is most likely due to the fact that reference [55] uses the average mileage of passenger cars in all of Germany, which is significantly higher than the mileage of passenger cars in Berlin [33,34].
The author of [56] determines the power demand of BEVs in German urban areas.Analogous to our approach, the German household travel survey provides the data basis for simulating the driving behaviour of the BEVs.The temporal distribution of BEV charging power demand is determined for two charging scenarios assuming a constant charging power of 11 kW.
Scenario 1: all vehicles are charged exclusively at their users' residences.Due to similar assumptions, the results obtained for scenario 1 are comparable to the temporal charging power demand we determined for the residences for the home-charging scenario (see Fig. 11(c)).Scenario 2: vehicles are charged at both the residences and the places of work.The results determined for scenario 2 are comparable to the total charging power demand we determined for the work-charging scenario (see Fig. 11(a)).
For scenario 1, the peak power demand can be observed at 6:00 PM.Due to the high simultaneity of the charging events, the required charging power starts to decrease sharply from 7:00 PM and is close to 0 kW per vehicle during the night hours.As a result of this high simultaneity, the peak power demand of 0.5 kW per vehicle in the study is slightly higher than the 0.31 kW per vehicle we determined in this paper (see Fig. 14(b)).The high simultaneity of the charging events is not discussed in the study.One reason for this could be the simulation condition that forces all BEVs to arrive back at their owners' residences on the same day they left.
For scenario 2, the study identifies a power demand curve that reaches its global maximum around 8:30 AM (0.65 kW per vehicle), then decreases until around 11:00 AM before rising again slightly and reaching a local maximum around 4:00 PM.During the night-time hours, the power demand is again close to 0 kW per vehicle.In contrast, in this paper we show that peak power demand is reached as early as 7:30 AM and then stagnates at this level until 9:00 AM, as BEVs that start charging and those that stop charging balance each other out.Although we assume a charging capacity of 22 kW at employee parking spots, we determine a lower maximum power demand per vehicle of 0.32 kW.This discrepancy is most likely also due to the high simultaneity of the charging events in the study as well.
In [57], the energy demand resulting from the electrification of passenger cars in Stuttgart, Germany and its surrounding areas is determined.Analogous to our approach, the driving behaviour of BEVs is modeled based on a travel survey.In the study, vehicles are charged as soon as their SOC value is below 50%.Charging power at private parking spots at residential buildings is assumed to be 3.7 kW and 50 kW at all other locations (roadside, workplaces, etc.).Due to similar assumptions, the results of the study can be compared to the total charging power demand we determined for the data-driven charging scenario.This comparison shows similar results for the daytime.The power demand peak is observed around 9:00 AM, which is mainly due to charging at the places of work.After this peak, power demand decreases before increasing again in the evening hours due to charging at residences.However, in contrast to our results the study identifies a power demand of nearly 0 kW per vehicle between 4:00 AM and 5:00 AM.This low power demand in the night is not discussed.One possible reason for this could be the simulation condition that forces all BEVs to arrive back at their owners' residences on the same day they left.Another reason could be that the charging events are terminated more quickly since the study assumes a charging power of 50 kW at roadside parking spots.
In addition, differences in peak power demand can be observed.While the peak power demand calculated in this paper is 0.37 kW per vehicle, it is 0.54 kW per vehicle in the study (see Fig. 14(c)).This higher demand is most likely due to the higher car usage in Stuttgart (58% of all trips) [58] compared to Berlin (34%) [34].As a result, peak power demand is higher.A higher peak power demand per vehicle also results from the fact that the study assumes a charging power of 50 kW, which is higher than in our work (22 kW at employee parking spots and 11 kW at roadside parking spots).Ref. [59] presents the results of an experimental study on BEV usage behaviour of 10 households and their 11 BEVs, conducted in Stuttgart, Germany.The BEVs in the study were charged exclusively at residences; accordingly, the results are comparable to the residential charging power demand we determined for the home-charging scenario.The temporal distribution of charging power demand in the study is similar to our results, showing highest demand at 9:00 PM and lowest demand at 9:00 AM.In the study, the minimum power demand is 43% of the peak power demand.This is higher than our results, where the minimum demand is 22.8% of the peak demand.The difference is most likely due to the overrepresentation of pensioners among the study participants.In particular, pensioners do not have the "typical" daily routine of going to work in the morning and returning in the evening.As a result, charging events are much more evenly distributed throughout the day.
Overall, it can be stated that our results show some deviations from the existing literature, but are in overall agreement with it.The deviations can be plausibly justified by methodological differences and deviating parameters.Therefore, the results of this paper can be considered valid.

Conclusions and outlook
To support power grid operators in detecting and evaluating potential power grid congestions due to the electrification of urban private cars, accurate models are needed to determine BEV charging energy and power demand with high spatial and temporal resolution.Typically, activity-based mobility models are used for this purpose, with detailed travel surveys forming the data basis.From these surveys, activity-and time-dependent traffic flows between sub-areas in the considered area can be directly determined, which in turn can be used to derive BEV charging demand.However, detailed travel surveys are typically not available for most places in the world.
To address this research gap, we developed an activity-based model for estimating the spatial and temporal distribution of BEV charging demand that does not require detailed travel surveys as input parameters.The method is based on individual, full-day travel schedules for each vehicle in the considered area, which provide information on the sequence of activities and trips between these activities [15].Since the locations where activities are performed are not included in these travel schedules, we developed a route assignment method in this paper to determine the unknown activity locations.
We applied our approach to the urban area of Berlin and its 448 subdistricts.Assuming full electrification of the 1,045,000 private cars in Berlin, we determined both the required BEV charging energy demand and the power demand over the course of the day for each district.Since the developed method operates at the vehicle level, it can also be used to determine BEV charging energy demand for lower levels of electrification (e.g.50%).
The method is based on open data (e.g.OpenStreetMap and publicly available statistics), therefore it is transferable to other urban regions.
On the basis of our results, load shifting potentials can be investigated.Compared to uncontrolled charging, we show for an exemplary district that it is theoretically possible to reduce peak power demand at residences by up to 31.7% through load shifting.In addition, we show that the peak-to-average power ratio can be significantly reduced.Since load shifting is often easier and cheaper to implement (e.g., via price incentives) than grid expansion, grid expansion should only take place if no further load shifting potential exists.In addition to load shifting, the results of this paper can also be used to investigate vehicle-to-grid potential in an urban area, which will be part of future work.
In Germany, only 0.64% of passenger cars were battery electric at the end of 2021 [60].Accordingly, there is no data on the charging behavior of BEV users in Germany or Berlin.BEV charging demand was therefore determined for four different charging scenarios in this paper.As soon as data on charging behavior in Germany is available, the BEV charging demand for Berlin should be recalculated and compared with the results of the four scenarios.
We have validated our results by comparing them with similar studies.However, since the results are forecasts, it is desirable to compare them with exhaustive data.This requires extensive measurement campaigns in which both the routes and the charging behaviour of BEVs are recorded.

Fig. 1 .
Abbreviations BEV Battery electric vehicle ICEV Internal combustion engine vehicle O-D Origin-destination LOR Lebensweltlich orientierter Raum (neighborhood oriented district) SOC State of charge

Fig. 5 .
Fig. 5. Travel speed criterion.(a) Correlation between travel distance and travel speed for 2 origin-destination LOR combinations.(b) Division of the calculated travel speeds in Berlin into 10 bins and corresponding rating value k s .

Fig. 4 .
Fig. 4. Travel distance criterion.(a) Location of the origin LOR and the three destination LORs in Berlin.(b) Division of computed travel distances into 20 bins and corresponding rating value k d .

Fig. 7 .
Fig. 7. Route assignment procedure for an example vehicle.(a) Rating of the possible destinations.(b) Selection of the most probable route.

Fig. 8 .
Fig. 8. Data-driven charging scenario.Charging behaviour of the BEVs, according to Beijing dataset [51].(a) SOC at the first trip of the day.(b) Rechargeable SOC difference at charging event.

Fig. 9 .
Fig. 9. Data-driven charging scenario.Method for determining the charging behaviour of a BEV.

Fig. 10 .
Fig. 10.Spatial distribution of the BEV charging energy demand in the Berlin LORs -Data-driven charging scenario.(a) Energy demand at places of work.(b) Energy demand at shopping locations.(c) Energy demand at residences.(d) Total energy demand.

Fig. 13 .
Fig. 13.Load shifting results in the LOR "Heiligensee" for the home-and data-driven charging scenario.(a) Power demand.Home-charging scenario.(b) Power demand.Data-driven charging scenario.

Fig. B. 2 .
Fig. B.2. Spatial temporal distribution of charging power demand at shopping locations in the Berlin LORs -Data-driven charging scenario.

Fig. B. 3 .
Fig. B.3.Spatial temporal distribution of charging power demand at residences in the Berlin LORs -Data-driven charging scenario.

Fig. B. 4 .
Fig. B.4. Spatial temporal distribution of the total charging power demand in the Berlin LORs -Data-driven charging scenario.

Table 1
BEV charging energy demand results for an average workday in Berlin by charging scenario.